The linear stress triangular equilibrium model in plane elasticity

Abstract

Advantage is taken of oblique coordinates to give a revised theory of the triangular equilibrium finite element model with linearly varying stresses for problems in plane linear elasticity. This new formulation has considerably improved computational efficiency over earlier derivations because equilibrium of the stresses within the element is enforced explicitly without recourse to the more expensive numerical methods used previously. The equilibrium model provides upper bounds to the elastic strain energy of a body under applied loading; it is the dual of a triangular finite element model with linear strains obtained from compatible quadratic displacements which provides corresponding lower bounds.